Investigation of the effective density of arbitrarily shaped plate-type acoustic metamaterials without mass attached

The effective densities of arbitrarily shaped plate-type acoustic metamaterials (AMMs) without mass attached are studied in this paper. Acoustic impedances of three different shaped plates, i.e. circle, triangle, and hexagon, are calculated by the meshless boundary method and the effective densities are calculated using the lumped model. To validate the accuracy of this framework, the numerical results are compared with the analytical solution as well as the finite element method (FEM) for circular plates and are compared with FEM for the other two shapes. In general, good agreements can be found provided that a sufficient number of edge points and collocation points are used in the meshless boundary method. For the triangular shape, some discrepancies are found at the low-frequency region and this might have been because of the sharp corners of the triangle. The framework studied in this paper can provide an accurate and efficient method for designing plate-type AMMs with an arbitrary shape.